Properties

Label 14400.q
Number of curves 2
Conductor 14400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.q1 14400s2 [0, 0, 0, -11340, -464400] [2] 24576  
14400.q2 14400s1 [0, 0, 0, -540, -10800] [2] 12288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.q have rank \(0\).

Modular form 14400.2.a.q

sage: E.q_eigenform(10)
 
\( q - 4q^{7} + 4q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.